Automorphism groups of finite dimensional simple algebras
نویسندگان
چکیده
منابع مشابه
Finite dimensional graded simple algebras
Let R be a finite-dimensional algebra over an algebraically closed field F graded by an arbitrary group G. We prove that R is a graded division algebra if and only if it is isomorphic to a twisted group algebra of some finite subgroup of G. If the characteristic of F is zero or char F does not divide the order of any finite subgroup of G then we prove that R is graded simple if and only if it i...
متن کاملSimple Finite-dimensional Double Algebras
A double algebra is a linear space V equipped with linear map V ⊗ V → V ⊗ V . Additional conditions on this map lead to the notions of Lie and associative double algebras. We prove that simple finite-dimensional Lie double algebras do not exist over an arbitrary field, and all simple finite-dimensional associative double algebras over an algebraically closed field are trivial. Over an arbitrary...
متن کاملAutomorphism groups of finite posets
For any finite group G, we construct a finite poset (or equivalently, a finite T0-space) X, whose group of automorphisms is isomorphic to G. If the order of the group is n and it has r generators, X has n(r+2) points. This construction improves previous results by G. Birkhoff and M.C. Thornton. The relationship between automorphisms and homotopy types is also analyzed.
متن کاملA characterization of simple $K_4$-groups of type $L_2(q)$ and their automorphism groups
In this paper, it is proved that all simple $K_4$-groups of type $L_2(q)$ can be characterized by their maximum element orders together with their orders. Furthermore, the automorphism groups of simple $K_4$-groups of type $L_2(q)$ are also considered.
متن کاملCompact automorphism groups of vertex operator algebras
Let V be a simple vertex operator algebra which admits the continuous, faithful action of a compact Lie group G of automorphisms. We establish a Schur-Weyl type duality between the unitary, irreducible modules for G and the irreducible modules for V G which are contained in V where V G is the space of G-invariants of V. We also prove a concomitant Galois correspondence between vertex operator s...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annals of Mathematics
سال: 2003
ISSN: 0003-486X
DOI: 10.4007/annals.2003.158.1041